A family of evolution equations connecting area-preserving to length-preserving curve flows. (October 2018)

• Record Type: Journal Article
• Authors: Guo, Hongxin; Sun, Zezhen
• Is Part Of: Nonlinear analysis. Volume 43(2018)
• Page Start: 515
• Page End: 522
• Publication Date: 2018-10
• Subjects: Curve shortening flow -- Isoperimetric inequality -- Convex curves; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.03.012
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we define a one parameter family of curve flows in the plane connecting a type of area-preserving to length-preserving curve flows. When the initial curve is closed and convex, we show that along the flows the length of the curve is non-increasing while the enclosed area is non-decreasing. We show that the solutions exist for all time and converge to a circle in C 0 norm when t → + ∞ .